Author: Max Snow
link: https: //www.zhihu.com/question/304611853/answer/553540524
Source: know almost
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Cong view the entire history of physics, I think is not really shocking how complex formula becomes (geocentric and made quite complicated ...), but physics has become increasingly from straightforward .
Newton periods:
Newton ancestors really off to a good start ah, in order to establish their first engage in physical theory out calculus, initially regarded as a model of a combination of mathematics and physics, the simple formula can predict the next three celestial movement can explain the slopes small slider is really not satisfied.
Newtonian mechanics is the basic physical spatial coordinates x, time t, mass m, as well as energy, these amounts can be very normal people intuitively understand what it means, it is often used in natural language.
And this thing is intuitive calculus is also very good, think we solve the high number of problems when used in a lot of thinking in images, for example, we can be understood as a small differential, integral understood as the sum, think, and elementary mathematics not much differences.
After Newton's time:
After Newton is statistical mechanics, Maxwell's electromagnetism, analytical mechanics these. Although these theories to some extent independent of Newtonian mechanics, but there is no contradiction between Newtonian mechanics and the fundamental view of the world. And these mathematical theory but is also required elementary mathematics + calculus.
Which is the basic physical electromagnetism electric and magnetic fields, the introduction of statistical mechanics entropy, the amount of heat which, in general, or intuitive Leverage. The more subtle analytical mechanics, although the theoretical system and Newtonian mechanics is completely equivalent, but at the Lagrangian and Hamiltonian basic physical reason for the definition of these two quantities completely out of considerations of mathematics, not intuitive . The two brothers later proved played an extremely important role in modern physics.
Einstein period:
Since Einstein comes to the world of physics began to develop abnormal direction. . .
In Newton's time, it is the first intuitive physics before they developed a mathematical need. Einstein period on the contrary, there are some blind just before mathematicians play things, had not felt the real world and there is nothing in this period was the introduction of physics, specifically refers to the differential manifold, group theory and so on.
Special theory of relativity tells us that time and space quite position, are components of four-dimensional space vector switching inertial system of four-dimensional space is in fact rotate, we can rotate a three-dimensional analogy to understand. And momentum wave vector, the electromagnetic field can be found corresponding to these quantities Covariant form.
General relativity tells us that time and space is not flat but twisted together, the reason why we feel is flat simply because the density is not particularly large things around us so space-time bending effect is not obvious (of course this is the cause of the Earth in space and time said bending interpreted as gravitational premise), time and space for the first time undergone such a profound relevance in physics! Description of real time and space is not Euclidean geometry, but Riemannian (Kant anger hit the face). Overall, the Einstein differential manifold language replaces the normal understanding of space and time naive, we found that the intuitive thing to take for granted is not necessarily really right (as in geometry axiom of parallels in the real world not right). But we can be intuitive 2D and 3D space bending to understand the curved four-dimensional space. In addition to highlighting the geometry of spacetime outside, the theory of relativity does not introduce any fundamental physical quantities and more than Newtonian mechanics, just the physical organized into Lorentz covariant form.
And then say quantum mechanics, even though this guy used the mathematical theory of general relativity is not complicated, but it is really a counter-intuitive.
1. It follows the analysis of Hamiltonian mechanics inside, the concept of generalized coordinates.
2. Newtonian coordinates and velocity with which to describe the state of a particle, and a particle that is not quantum mechanics has determined coordinates and velocity, the wave function is thus characterized by state of the particles, the mold wave function is a probability density of particles Founder distributed. In addition to the coordinate and momentum, other physical quantities is probabilistic.
3. Quantum mechanics is the number of the physical quantity is not considered, but the operator, or linear algebra inside linear transformation (HERMITE a), (Equation in two positions so that the physical quantity can not be freely exchanged according to multiply as before commutative) algebra for the first time in which physics is referred to such a high position!
4. The use of linear algebra it is not on the real line represents the most undergraduate science field, but in the complex domain. Yes, there Schrodinger equation containing the basic equations of quantum mechanics imaginary! Electrodynamics in different kind of imaginary numbers for convenience of calculation introduced quantum mechanics itself requires a complex structure! Imaginary seems impossible physically meaningful actually appeared inside the basic equation, this is how crazy!
Quantum Field Theory periods:
Field theory is the basic language of modern physics. Wherein the basic physical quantity called the field operator, including scalar field and vector field Rotational Field. Scalar field defined Free theory is this: . If the quantum mechanical wave function inside can also be established directly by the probability density, now that the field operator really intuitive are gone (actually it should be understood as a superposition of harmonic oscillator whole lot, but I think for it is very hard to accept, who cares resonator ah ..orz), a big advantage of this definition is its transformation properties under Lorentz transformations and general scalar field the same.
When we learn of special relativity the Lorentz transformation is generally understood as some fixed four-dimensional matrix, but in the field theory of spin (spin) concept allows us to recognize, really the most important thing is not that Lorentz matrix, but behind the Matrix Lie Algebra , or a Lorentz group. That matrix is just a four-dimensional Lorentz group representation (representation), but rather the amount of such two-dimensional spin like something is transformed in accordance with the two-dimensional representation. How Before the establishment of relativistic quantum mechanics, whether mathematicians or ordinary people, who would have thought such a highly abstract group theory and the nature of things can have such a deep connection?
Field theory understanding of what particles are also highly abstract, is not what we usually had in mind a small ball, and I quote Schwartz textbook in the words:. Particles transform under irreducible unitary representations of the Poincare group This statement can even be interpreted as the definition of what a particle is. a lot of people are always curious antiparticles in the end is valid and what, in fact, field theory, the definition of antiparticles is purely abstract, no one can intuitively tell you why the existence of antiparticles.
In addition, field theory the importance of symmetry referred to an unprecedented height, a Lagrangian is the reason why it is the way, is usually for reasons of symmetry (including Lorentz invariance) of. Obviously this is a mathematical reason rather than an intuitive reason.
After then is string theory, yet I do not know I will not say.
to sum up:
We could say that the history of physics is to abstract from the intuitive development trends. Mathematics and physics unified so deep, beyond the physics of any natural science, social science, engineering, business, have not this is theoretical physics for me the most shocking place appeared. For this reason, mathematics and physics in my mind is the unity of human civilization, the most shining star in one of two.
